Question

A farmer in Addison County has 600 acres of land that can be used to grow corn

and/or soybeans. The net profit per acre is $60 for soybeans and $55 for corn. In addition to   

the land constraint, the farmer has limited labor resources: 200 hours of labor available for

planting, and 300 hours of labor available for cultivation. Labor required for planting is 0.6

hour per acre for corn and 0.7 hour per acre for soybeans. Cultivation is only necessary for

corn production which requires 0.5 hour per acre. Also, corn yield is known to be 70

bushels per acre and the farmer does not want to produce more than 21,000 bushels of corn

due to the limited storage space. Develop a linear programming (LP) model for the farmer  

to maximize the total profit (you do not need to solve your LP model) in three steps

(1)

(2)

(3)

Answer 1

Step 1: Let the number of acres for Corn be x and acres for soybean be y

Step 2: Total Profit = 55x + 60y

We have to maximize this profit. hence, we get objective function as

Maximize Total profit P = 55x + 60y

Step 3: Subject to constraints:

x + y <= 600.......................Constraint for the total availability of acres of land

0.6*x + 0.7y <= 200............Constraint for the total availability of Planting hours

0.5y <= 300........................Constraint for the total availability of cultivation hours

70x <= 21000.....................Constraint for maximum no. of bushels produced for corn

x, y >= 0..............................Non-negativity constraints as no. of acres cannot be negative.

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